复分析:可视化方法

复分析
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作者: (Tristan Needham)
出版社: 人民邮电出版社
2007-02
版次: 1
ISBN: 9787115155160
定价: 79.00
装帧: 平装
开本: 16开
纸张: 胶版纸
页数: 592页
字数: 857千字
正文语种: 英语
原版书名: Visual Complex Analysis
  •   《复分析:可视化方法(英文版)》是复分析领域近年来较有影响的一本著作。作者用丰富的图例展示各种概念、定理和证明思路,十分便于读者理解,充分揭示了复分析的数学之美。书中讲述的内容有几何、复变函数变换、默比乌斯变换、微分、非欧几何、复积分、柯西公式、向量场、复积分、调和函数等。   TristanNeedham,旧金山大学教授系教授,理学院副院长。牛津大学博士,导师为RogerPenrose(与霍金齐名的英国物理学家)。因本书被美国数学会授予CarlB.Allendoerfer奖。他的研究领域包括几何、复分析、数学史、广义相对论。 1GeometryandCompleXArIthmetIc
    1IntroductIon
    2EulersFormula
    3SomeApplIcatIons
    4TransformatIonsandEuclIdeanGeometry*
    5EXercIses

    2CompleXFunctIonsasTransformatIons
    1IntroductIon
    2PolynomIals
    3PowerSerIes
    4TheEXponentIalFunctIon
    5CosIneandSIne
    6MultIfunctIons
    7TheLogarIthmFunctIon
    8AVeragIngoVerCIrcles*
    8EXercIses

    3M?bIusTransformatIonsandInVersIon
    1IntroductIon
    2InVersIon
    3ThreeIllustrativeApplIcatIonsofInVersIon
    4TheRIemannSphere
    5M?bIusTransformatIons:BasIcResults
    6M?bIusTransformatIonsasMatrIces*
    7VisualIzatIonandClassIfIcatIon*
    8DecomposItIonInto2or4ReflectIons*
    8AutomorphIsmsoftheUnItDIsc*
    9EXercIses

    4DIfferentIatIon:TheAmplItwIstConcept
    1IntroductIon
    2APuzzlIngPhenomenon
    3LocalDescrIptIonofMappIngsInthePlane
    4TheCompleXDerivativeasAmplItwIst
    5SomeSImpleEXamples
    6Conformal=AnalytIc
    7CrItIcalPoInts
    8TheCauchy-RIemannEquatIons
    8EXercIses

    5FurtherGeometryofDIfferentIatIon
    1Cauchy-RIemannReVealed
    2AnIntImatIonofRIgIdIty
    3VisualDIfferentIatIonoflog(z)
    4RulesofDIfferentIatIon
    5PolynomIals,PowerSerIes,andRatIonalFunc-tIons
    6VisualDIfferentIatIonofthePowerFunctIon
    7VisualDIfferentIatIonofeXp(z)231
    8GeometrIcSolutIonofE=E
    8AnApplIcatIonofHIgherDerivatives:CurVa-ture*
    9CelestIalMechanIcs*
    10AnalytIcContInuatIon*
    11EXercIses

    6Non-EuclIdeanGeometry*
    2IntroductIon
    2SpherIcalGeometry
    3HyperbolIcGeometry
    4EXercIses

    7WIndIngNumbersandTopology
    1WIndIngNumber
    2HopfsDegreeTheorem
    3PolynomIalsandtheArgumentPrIncIple
    4ATopologIcalArgumentPrIncIple*
    5RouchésTheorem
    6MaXImaandMInIma
    7TheSchwarz-PIckLemma*
    8TheGeneralIzedArgumentPrIncIple

    8EXercIses
    8CompleXIntegratIon:CauchysTheorem
    2ntroductIon
    2TheRealIntegral
    3TheCompleXIntegral
    4CompleXInVersIon
    5ConjugatIon
    6PowerFunctIons
    7TheEXponentIalMappIng
    8TheFundamentalTheorem
    8ParametrIcEValuatIon
    9CauchysTheorem
    10TheGeneralCauchyTheorem
    11TheGeneralFormulaofContourIntegratIon

    11EXercIses
    9CauchysFormulaandItsApplIcatIons
    1CauchysFormula
    2InfInIteDIfferentIabIlItyandTaylorSerIes
    3CalculusofResIdues
    4AnnularLaurentSerIes
    5EXercIses

    10VectorFIelds:PhysIcsandTopology
    1VectorFIelds
    2WIndIngNumbersandVectorFIelds*
    3FlowsonClosedSurfaces*
    4EXercIses

    11VectorFIeldsandCompleXIntegratIon
    1FluXandWork
    2CompleXIntegratIonInTermsofVectorFIelds
    3TheCompleXPotentIal
    4EXercIses

    12FlowsandHarmonIcFunctIons
    1HarmonIcDuals
    2ConformalInVarIance
    3APowerfulComputatIonalTool
    4TheCompleXCurVatureReVIsIted*
    5FlowAroundanObstacle
    6ThePhysIcsofRIemannsMappIngTheorem
    7DirichletsProblem
    8ExercIses
    References
    IndeX
  • 内容简介:
      《复分析:可视化方法(英文版)》是复分析领域近年来较有影响的一本著作。作者用丰富的图例展示各种概念、定理和证明思路,十分便于读者理解,充分揭示了复分析的数学之美。书中讲述的内容有几何、复变函数变换、默比乌斯变换、微分、非欧几何、复积分、柯西公式、向量场、复积分、调和函数等。
  • 作者简介:
      TristanNeedham,旧金山大学教授系教授,理学院副院长。牛津大学博士,导师为RogerPenrose(与霍金齐名的英国物理学家)。因本书被美国数学会授予CarlB.Allendoerfer奖。他的研究领域包括几何、复分析、数学史、广义相对论。
  • 目录:
    1GeometryandCompleXArIthmetIc
    1IntroductIon
    2EulersFormula
    3SomeApplIcatIons
    4TransformatIonsandEuclIdeanGeometry*
    5EXercIses

    2CompleXFunctIonsasTransformatIons
    1IntroductIon
    2PolynomIals
    3PowerSerIes
    4TheEXponentIalFunctIon
    5CosIneandSIne
    6MultIfunctIons
    7TheLogarIthmFunctIon
    8AVeragIngoVerCIrcles*
    8EXercIses

    3M?bIusTransformatIonsandInVersIon
    1IntroductIon
    2InVersIon
    3ThreeIllustrativeApplIcatIonsofInVersIon
    4TheRIemannSphere
    5M?bIusTransformatIons:BasIcResults
    6M?bIusTransformatIonsasMatrIces*
    7VisualIzatIonandClassIfIcatIon*
    8DecomposItIonInto2or4ReflectIons*
    8AutomorphIsmsoftheUnItDIsc*
    9EXercIses

    4DIfferentIatIon:TheAmplItwIstConcept
    1IntroductIon
    2APuzzlIngPhenomenon
    3LocalDescrIptIonofMappIngsInthePlane
    4TheCompleXDerivativeasAmplItwIst
    5SomeSImpleEXamples
    6Conformal=AnalytIc
    7CrItIcalPoInts
    8TheCauchy-RIemannEquatIons
    8EXercIses

    5FurtherGeometryofDIfferentIatIon
    1Cauchy-RIemannReVealed
    2AnIntImatIonofRIgIdIty
    3VisualDIfferentIatIonoflog(z)
    4RulesofDIfferentIatIon
    5PolynomIals,PowerSerIes,andRatIonalFunc-tIons
    6VisualDIfferentIatIonofthePowerFunctIon
    7VisualDIfferentIatIonofeXp(z)231
    8GeometrIcSolutIonofE=E
    8AnApplIcatIonofHIgherDerivatives:CurVa-ture*
    9CelestIalMechanIcs*
    10AnalytIcContInuatIon*
    11EXercIses

    6Non-EuclIdeanGeometry*
    2IntroductIon
    2SpherIcalGeometry
    3HyperbolIcGeometry
    4EXercIses

    7WIndIngNumbersandTopology
    1WIndIngNumber
    2HopfsDegreeTheorem
    3PolynomIalsandtheArgumentPrIncIple
    4ATopologIcalArgumentPrIncIple*
    5RouchésTheorem
    6MaXImaandMInIma
    7TheSchwarz-PIckLemma*
    8TheGeneralIzedArgumentPrIncIple

    8EXercIses
    8CompleXIntegratIon:CauchysTheorem
    2ntroductIon
    2TheRealIntegral
    3TheCompleXIntegral
    4CompleXInVersIon
    5ConjugatIon
    6PowerFunctIons
    7TheEXponentIalMappIng
    8TheFundamentalTheorem
    8ParametrIcEValuatIon
    9CauchysTheorem
    10TheGeneralCauchyTheorem
    11TheGeneralFormulaofContourIntegratIon

    11EXercIses
    9CauchysFormulaandItsApplIcatIons
    1CauchysFormula
    2InfInIteDIfferentIabIlItyandTaylorSerIes
    3CalculusofResIdues
    4AnnularLaurentSerIes
    5EXercIses

    10VectorFIelds:PhysIcsandTopology
    1VectorFIelds
    2WIndIngNumbersandVectorFIelds*
    3FlowsonClosedSurfaces*
    4EXercIses

    11VectorFIeldsandCompleXIntegratIon
    1FluXandWork
    2CompleXIntegratIonInTermsofVectorFIelds
    3TheCompleXPotentIal
    4EXercIses

    12FlowsandHarmonIcFunctIons
    1HarmonIcDuals
    2ConformalInVarIance
    3APowerfulComputatIonalTool
    4TheCompleXCurVatureReVIsIted*
    5FlowAroundanObstacle
    6ThePhysIcsofRIemannsMappIngTheorem
    7DirichletsProblem
    8ExercIses
    References
    IndeX
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